Optimal control problems for some reaction diffusion equations

In this talk we introduce the optimal control problems for some reaction diffusion equations, the chemotaxis equation and the forest kinematic equation etc. Those equations are non-linear parabolic equations mathematically. Therefore, by using Galerkin method, we show the existence and the uniqueness of solutions for the parabolic equations. Introducing the cost function, we show the existence of optimal control. And then we deduce the necessary conditions by showing the differentiability of state solution with respect to the control. Under some conditions, we show the uniqueness of the optimal controls.